In my research work I came across the following statement:
Let $B(m)$ be the transmitted symbols, $B(m)$ ∈ {-1,1}, for $m=1,2,...,1000$. Based on $B(m)$ is -1 or +1, we get two expressions as $\psi_{m,0} = h_m-\alpha f_mg_m$ and $\psi_{m,1} = h_m+\alpha f_mg_m$ where $\alpha = 0.5$, $h,f$ and $g$ are complex Gaussian random variables with zero mean and unit variance.
My query is $\psi_{m,0}$ and $\psi_{m,1}$ will be scalar or a vector. I am facing this confusion because in the next equations given in research paper, I have to deal with norm and Hermitian i.e., $||\psi_{m,0}^H||^2$ .
Any help in this regard will be highly appreciated.